1. Technical Field
This invention relates to an area cutting method and, more particularly, to an area cutting method for cutting the interior of an area bounded by a closed curve.
2. Description of the Related Art
Forms of numerically controlled machining include cutting in which the interior of an area bounded by a closed curve is hollowed out down to a predetermined depth, and die milling in which the interior of an area is die milled. In such machining, as shown in FIG. 9(A), an area cutting method is conventionally carried out by performing cutting along an (i-1)th cutting path PTi-1 in one direction (the direction of the solid line arrow), raising the tool a predetermined amount at the completion of cutting, then positioning the tool directly above a cutting starting point Ps on the next, or i-th, cutting path PTi, thereafter lowering the tool to the cutting starting point Ps, moving the tool along the i-th cutting path PTi in the direction of the solid line arrow, and subsequently repeating the above unidirectional cutting.
Another area cutting method shown in FIG. 9(B) includes, following completion of cutting along the cutting path PTi-1 of the (i-1)th cutting path, moving the tool from a cutting end point Pe to the cutting starting point Ps on the next, or i-th, cutting path, and thereafter performing cutting along the i-th cutting path PTi. Thus, cutting is performed back and forth in the direction of the arrows.
Still another area cutting method shown in FIG. 9(C) includes obtaining offset paths OFC1, OFC2, . . . OFCn offset by predetermined amounts with respect to a curve OLC of an external shape, and moving the tool successively along the offset paths.
However, with the first area cutting method based on unidirectional cutting, the tool must be positioned at the cutting starting point Ps on the i-th cutting path PTi after the completion of cutting along the (i-1)th cutting path PTi-1. This method is disadvantageous in that it results in a long tool traveling distance.
With the second cutting method based on reciprocative cutting, portions are left uncut. In order to cut the uncut portions, the tool must be moved along the external shape curve OLC at completion of the back-and-forth cutting, thereby necessitating both back-and-forth cutting control and cutting control along the shape of the external curve. Accordingly, this method is disadvantageous in that control is complicated. Further, if an area AR has concavities and convexities, as shown in FIG. 9(D), the second method requires movement for achieving positioning indicated by the dashed lines. This is disadvantageous in that tool travelling distance and cutting time are prolonged. In addition, since the cutting process for the outward trip is different from the cutting process for the return trip, cutting cannot be performed efficiently overall. It should be noted that the cutting processes referred to here indicate up cutting and down cutting processes. FIGS. 10(A), (B) show examples of the down cutting process, and FIGS. 10(C), (D) depict examples of the up cutting process. If the workpiece material has been decided, then a cutting method capable of cutting the workpiece efficiently is selected from the up cutting and down cutting processes. However, with the second method, the up cutting process [e.g. FIG. 10(A)] and the down cutting process [e.g. FIG. 10(C)] are always mixed, so that cutting cannot be performed efficiently.
With the third method of cutting along the offset paths, portions are left uncut at, e.g., the central portion of the area, depending upon the contour of the external shape curve. This method is disadvantageous in that dealing with these uncut portions is a complicated task.
Accordingly, in order to eliminate the aforementioned drawbacks of the conventional method, the applicant has proposed a method in which a tool path in the form of a spider web pattern is decided within the area and a tool is moved along the tool path to machine the area. (For example, refer to the specification of U.S. Ser. No. 744,746, now U.S. Pat. No. 4,621,959.) FIGS. 11(A), (B) are views for describing this area cutting method. The area cutting method is composed of the following steps:
(1) For cutting the interior of an area AR bounded by an external shape curve OLC comprising a number of straight lines S1, S2, . . . S6 and a circular arc A1, linearly approximating a circular arc portion A1' of an offset curve OFC offset a predetermined amount from the external shape curve;
(2) dividing an area bounded by the linearly approximated offset curve into a plurality of convex polygons PG1-PG3;
(3) calculating the centroid Wi of each convex polygon and the mid-points M1, M2 of boundary lines B1, B2 of two mutually adjacent convex polygons and generating a base line BL obtained by successively connecting each centroid and each mid-point;
(4) partitioning, into a predetermined number of partitions, straight lines L1-L14 connecting the centroids Wi of the convex polygons and the apices P1-P10 of the convex polygons, and straight lines BL1-BL4 connecting the mid-points M1, M2 and the two ends P1, P4; P4, P7 of the boundary lines bisected by the mid-points;
(5) moving a tool along plural closed paths CPT1, CPT2, . . . obtained by connecting partitioning points P.sub.a1, P.sub.a2, . . . P.sub.a18 ; P.sub.b1, P.sub.b2, . . . P.sub.b18 [see FIG. 11(B)], which correspond to the straight lines L1-L14, BL1-BL4, in such a manner that the base line BL is enclosed, and moving the tool along the base line BL, and
(6) moving the tool along the offset curve OFC.
According to this method, area cutting can be carried out while moving the tool continuously. This is advantageous in that it eliminates wasted tool movement and shortens cutting time in comparison with the prior-art method. It also does not leave any uncut portions at, e.g., the central part of the area.
In accordance with this proposed method of cutting an area in a spider web-like pattern, however, if the shape of the area is a concave polygon, the area is always divided into a plurality of convex polygons and area cutting is performed upon deciding the tool paths based on each convex polygon.
However, there are cases where it is unnecessary to divide an area into convex polygonal portions even if the shape of the area is a concave polygon. In other words, there are cases where tool paths in the form of a spider web pattern can be decided without dividing an area into convex polygons even if the shape of the area is a concave polygon. Nevertheless, in the prior art, such an area is still divided into a plurality of convex polygons and tool paths are decided based on these convex polygons. For this reason, the processing for deciding the tool paths is complicated and an extended period of time is required to decide the tool paths.
Accordingly, an object of the present invention is provide a method through which an area can be cut upon deciding tool paths having the form of a spider web pattern without dividing the area into a plurality of convex polygons, even if the shape of the area is a concave polygon.
Another object of the present invention is to provide an area cutting method through which tool paths for cutting an area can be decided with ease in a short period of time.